Mitral regurgitation, also known as mitral insufficiency or mitral incompetence, is a heart condition in which the mitral valve does not close properly. This results in abnormal leakage of blood retrograde from the left ventricle through the mitral valve back upstream into the atrium. Persistent mitral regurgitation can result in congestive heart failure. Traditional surgical repair of the valve generally results in a good clinical outcome but requires open heart surgery and a lengthy and costly hospital stay with an extended recovery period. More recently, minimally invasive procedures have been developed to deliver a prosthetic heart valve percutaneously over a catheter through the patient's vasculature to the heart. Alternatively, a transapical procedure is used to introduce the prosthesis through the chest wall and through the apex of the heart. An exemplary prosthesis includes that described in U.S. Pat. No. 8,579,964, the entire contents of which are incorporated herein by reference in their entirety for all purposes. These prostheses and delivery procedures appear to be promising, but in certain circumstances they may obstruct blood flow, cause blood flow through the prosthesis to be turbulent, or disrupt the natural flow path, thereby potentially resulting in hemodynamic problems. Therefore, it would be desirable to provide improved devices, systems, and methods that avoid obstructing blood outflow and that maintain the natural flow path and natural hemodynamics. At least some of these objectives may be met by the exemplary embodiments described herein.